Boston’s attempt to clinch the Atlantic Division crown in the Knicks’ house Tuesday night came crashing down under a hail of 3-pointers and a rare offensive explosion by Mike Woodson’s Knicks.

A triple tag-team of Carmelo Anthony and reserves J.R. Smith and Steve Novak buried the Celtics in a rollicking, 118-110 victory at the giddy Garden, keeping the Knicks’ slim division title hopes alive for at least another couple of days.

Anthony posted his second career triple-double, with 35 points, 12 rebounds and 10 assists, many of them occurring on Novak and Smith bombs. Anthony’s only other triple-double came with Denver in 2007.

Smith and Novak each had 25 points off the bench and the trio led the Knicks to a wild, season-high 72-point first half. Center Tyson Chandler also contributed 20 points, dominating inside with nine of 10 buckets.

”I had nine and nine before,’’ Anthony said. “I’ve been missing it throughout my whole career. But tonight, coming into a game like this, it wasn’t me. It was Novak and J.R. making those shots. They wouldn’t have made the shots, I wouldn’t have had the triple-double.’’

Novak finished 8-of-10 from 3-point land, including back-to-back triples that knocked the Celtics out for good in the final three minutes. Smith was 7 of 10 from beyond the arc and scored 21 first-half points. The Knicks bagged 19 triples on the night — one off their franchise record — in a dizzying display reminiscent of the Mike D’Antoni era.

“He is the best 3-point shooter in our league,’’ Smith said of Novak. “It is not even close. People are starting to catch on to it, but not fast enough. To be honest, when I get the ball, he’s the first person I’m trying to find.’’

The victory pulled the Knicks within three games of the Celtics in the loss column of the Atlantic Division standings with five games remaining. The Knicks will have to win out to get there, but they mathematically stayed alive. For now, the Knicks (32-29) are in seventh place and would line up against the Heat in the opening round of the playoffs.

Smith said he and Novak battle in 3-point shooting contests during practice.

“It’s fun and he does actually win,’’ Smith said. “Even today, I was 7-of- 10. He was 8-of-10. He won again.’’

As the 3-point bombs fell in the first half, with the Knicks making 14 of 21 and building a 72-53 lead, the Garden was at its loudest all season.

“The fans really get into it,’’ Smith said. “You can feel the roar. It is a great feeling. When you are playing at home, it is great, period, when you play here at the Garden. It is indescribable.’’

Paul Pierce led a second-half comeback and finished with 43 points, getting Boston as close as six points in the fourth quarter, but Novak’s back-to-back treys crushed the comeback attempt. With Novak and Smith sizzling, the Knicks’ bench outscored Boston’s by an embarrassing 57-2.

“That’s been our M.O. for a while,’’ Novak said. “To have the bench come in and give us a boost, that’s when we’re at our best. That’s a pretty big number there.’’

The Celtics needed a victory over the Knicks and the Sixers to lose in Indiana to clinch their fifth straight Atlantic title but got just one of those to happen. With the Sixers’ loss, the Knicks now lead eighth-place Philadelphia by one game and own the tiebreaker. The Knicks also solidified their stronghold on a playoff spot, moving 2 ½ games ahead of the ninth-place Bucks.

“It took a lot to beat those guys,’’ Anthony said. “They never quit. Pierce kept them in it. But our bench played phenomenal. When they get hot like that, it’s hard to beat us.’’

The blazing Knicks racked up a 66.7 shooting percentage as they took a 72-53 lead at half. The 72 points was just 13 points less than their entire total Sunday in a discouraging 93-85 loss to Miami, when the club seemed genuinely worried the offense was over reliant on Anthony.

But with Anthony drawing extra attention from the Boston defense, it allowed Novak, in particular, to roam free.

“When Melo demands attention, it’s not crazy for the team to continue to put attention on him,’’ Novak said. “When someone winds up open, it’s really the product of them saying their game plan is to stop Melo.’’

The Celtics stopped nobody and, really, neither did the Knicks.

There wasn’t a lot of defense from both parties,’’ said a smiling Woodson, who improved to 10-1 at home and 14-5 as interim coach. “But it was nice to watch.’’

The former Denver duo, Anthony and Smith, combined for 40 first-half points and may have to put up similar numbers in the postseason if Amar’e Stoudemire cannot return to form.

“Melo is unbelievable the way he has been scoring the ball and getting to the hoop,’’ Novak said. “We are trying to make it harder for the defense to give him too much attention.’’

Anthony started the spree with 12 points in the first quarter , hitting 5-of-7 shots, sprinkling in jumpers and forays to the basket, taking advantage of his matchup against the bigger, slower Brendan Bass. Then came the second-quarter fireworks during which Smith couldn’t miss and the Knicks posted a 40-27 period, embarrassing the Celtics.

During that period, Novak completed a 4-point play, getting fouled and knocking hard into Woodson on the sidelines after draining a 3-pointer. Woodson went flying but caught Novak in his arms. Woodson rubbed Novak’s head and laughed. It was that kind of night.